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Chapter 4: Problem 21
Evaluate (if possible) the sine, cosine, and tangent at the real number. $$t=-\frac{3 \pi}{2}$$
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Write the function in terms of the sine function by using the identity $$A \cos \omega t+B \sin \omega t=\sqrt{A^{2}+B^{2}} \sin \left(\omega t+\arctan \frac{A}{B}\right).$$ Use a graphing utility to graph both forms of the function. What does the graph imply? $$f(t)=3 \cos 2 t+3 \sin 2 t$$
The numbers of hours \(H\) of daylight in Denver, Colorado, on the 15 th of each month are: \(1(9.67), 2(10.72), \quad 3(11.92), \quad 4(13.25)\) \(5(14.37), \quad 6(14.97), \quad 7(14.72), \quad 8(13.77), \quad 9(12.48)\) \(10(11.18), \quad 11(10.00), \quad 12(9.38) . \quad\) The month is represented by \(t,\) with \(t=1\) corresponding to January. A model for the data is \(H(t)=12.13+2.77 \sin \left(\frac{\pi t}{6}-1.60\right)\) (a) Use a graphing utility to graph the data points and the model in the same viewing window. (b) What is the period of the model? Is it what you expected? Explain. (c) What is the amplitude of the model? What does it represent in the context of the problem? Explain.
Is a degree or a radian the greater unit of measure? Explain.
Use a graphing utility to graph the function and the damping factor of the function in the same viewing window. Describe the behavior of the function as \(x\) increases without bound. $$h(x)=x \sin \frac{1}{x}$$
A car is moving at a rate of 65 miles per hour, and the diameter of its wheels is 2 feet. (a) Find the number of revolutions per minute the wheels are rotating. (b) Find the angular speed of the wheels in radians per minute.
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